Recommendation ITU-R P.681-11 (08/2019)

Propagation data required for the design systems in the land mobile-satellite service

P Series

Radiowave propagation

ii Rec. ITU-R P.681-11

Foreword

The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-

frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit

of frequency range on the basis of which Recommendations are adopted.

The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional

Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups.

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available from http://www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent

Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found.

Series of ITU-R Recommendations

(Also available online at http://www.itu.int/publ/R-REC/en)

Series Title

BO Satellite delivery

BR Recording for production, archival and play-out; film for television

BS Broadcasting service (sound)

BT Broadcasting service (television)

F Fixed service

M Mobile, radiodetermination, amateur and related satellite services

P Radiowave propagation

RA Radio astronomy

RS Remote sensing systems

S Fixed-satellite service

SA Space applications and meteorology

SF Frequency sharing and coordination between fixed-satellite and fixed service systems

SM Spectrum management

SNG Satellite news gathering

TF Time signals and frequency standards emissions

V Vocabulary and related subjects

Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1.

Electronic Publication

Geneva, 2019

ITU 2019

All rights reserved. No part of this publication may be reproduced, by any means whatsoever, without written permission of ITU.

Rec. ITU-R P.681-11 1

RECOMMENDATION ITU-R P.681-11*

Propagation data required for the design systems

in the land mobile-satellite service

(Question ITU-R 207/3)

(1990-1994-1995-1997-1999-2001-2003-2009-2015-2016-2017-2019)

Scope

This Recommendation predicts the various propagation parameters needed in planning systems in the land

mobile-satellite service (LMSS).

Keywords

Land mobile satellite channel, satellite to indoor channel, satellite diversity, urban environment,

shadowing, multipath, physical-statistical model

The ITU Radiocommunication Assembly,

considering

a) that for the proper planning of Earth-space land mobile systems it is necessary to have

appropriate propagation data and prediction methods;

b) that the methods of Recommendation ITU-R P.618 are recommended for the planning of

Earth-space telecommunication systems;

c) that further development of prediction methods for specific application to land mobile-

satellite systems is required to give adequate accuracy in all regions of the world and for all

operational conditions;

d) that, however, methods are available which yield sufficient accuracy for many applications,

recommends

that the methods contained in Annex 1 should be used in the planning of systems in the land mobile-

satellite service, in addition to the methods recommended in Recommendation ITU-R P.618.

Annex 1

1 Introduction

Propagation effects in the land mobile-satellite service (LMSS) differ from those of the fixed-satellite

service (FSS) primarily because of the greater importance of terrain effects. In the FSS it is generally

possible to discriminate against multipath, shadowing and blockage through the use of highly

directive antennas placed at unobstructed sites. Therefore, in general, the LMSS offers smaller link

* This Recommendation should be brought to the attention of Radiocommunication Study Group 4.

2 Rec. ITU-R P.681-11

availability percentages than the FSS. The prime availability range of interest to system designers is

usually from 80% to 99%.

This Annex deals with data and models specifically needed for predicting propagation impairments

in LMSS links, which include tropospheric effects, ionospheric effects, multipath, blockage and

shadowing. It is based on measurements ranging from 870 MHz in the UHF band up to 20 GHz.

2 Tropospheric effects

2.1 Attenuation

Signal losses in the troposphere are caused by atmospheric gases, rain, fog and clouds. Except at low

elevation angles, tropospheric attenuation is negligible at frequencies below about 1 GHz, and is

generally small at frequencies up to about 10 GHz. Above 10 GHz, the attenuation can be large for

significant percentages of the time on many paths. Prediction methods are available for estimating

gaseous absorption (Recommendation ITU-R P.676) and rain attenuation (Recommendation ITU-R

P.618). Fog and cloud attenuation is usually negligible for frequencies up to 10 GHz.

2.2 Scintillation

Irregular variations in received signal level and in angle of arrival are caused by both tropospheric

turbulence and atmospheric multipath. The magnitudes of these effects increase with increasing

frequency and decreasing path elevation angle, except that angle-of-arrival fluctuations caused by

turbulence are independent of frequency. Antenna beamwidth also affects the magnitude of these

scintillations. These effects are observed to be at a maximum in the summer season. A prediction

method is given in Recommendation ITU-R P.618.

3 Ionospheric effects

Ionospheric effects on Earth-to-space paths are addressed in Recommendation ITU-R P.531. Values

of ionospheric effects for frequencies in the range of 0.1 to 10 GHz are given in Tables 1 and 2 of

Recommendation ITU-R P.680.

4 Shadowing

4.1 Roadside tree-shadowing model

Cumulative fade distribution measurements at 870 MHz, 1.6 GHz and 20 GHz have been used to

develop the extended empirical roadside shadowing model. The extent of trees along the roadside is

represented by the percentage of optical shadowing caused by roadside trees at a path elevation angle

of 45° in the direction of the signal source. The model is valid when this percentage is in the range of

55% to 75%.

4.1.1 Calculation of fading due to shadowing by roadside trees

The following procedure provides estimates of roadside shadowing for frequencies between 800 MHz

and 20 GHz, path elevation angles from 7° up to 60°, and percentages of distance travelled from 1%

to 80%. The empirical model corresponds to an average propagation condition with the vehicle

driving in lanes on both sides of the roadway (lanes close to and far from the roadside trees are

included). The predicted fade distributions apply for highways and rural roads where the overall

aspect of the propagation path is, for the most part, orthogonal to the lines of roadside trees and utility

Rec. ITU-R P.681-11 3

poles and it is assumed that the dominant cause of LMSS signal fading is tree canopy shadowing (see

Recommendation ITU-R P.833).

Parameters required are the following:

f : frequency (GHz)

: path elevation angle to the satellite (degrees)

p : percentage of distance travelled over which fade is exceeded.

Step 1: Calculate the fade distribution at 1.5 GHz, valid for percentages of distance travelled of

20% p 1%, at the desired path elevation angle, 60 20:

AL( p,) – M() ln ( p) N() (1)

where:

M() 3.44 0.0975 – 0.002 2 (2)

N() – 0.443 34.76 (3)

Step 2: Convert the fade distribution at 1.5 GHz, valid for 20% p 1%, to the desired frequency,

f (GHz), where 0.8 GHz f 20 GHz:

ffpAfpA L

1–

15.1exp),(),,(

5.120 (4)

Step 3: Calculate the fade distribution for percentages of distance travelled 80% p 20% for the

frequency range 0.85 GHz f 20 GHz as:

pfAfpA

80ln

4ln

1),%,20(),,( 20 for 80% p 20% (5)

),,(20 fpA for 20% p 1%

Step 4: For path elevation angles in the range 20 7, the fade distribution is assumed to have

the same value as at 20.

Figure 1 shows fades exceeded at 1.5 GHz versus elevation angles between 10 and 60 for a family

of equal percentages between 1% and 50%.

4.1.1.1 Extension to elevation angles 60

The roadside shadowing model at frequencies of 1.6 GHz and 2.6 GHz can be extended to elevation

angles above 60 with the following procedure:

– apply equations (1) to (5) at an elevation angle of 60 at the above frequencies;

– linearly interpolate between the value calculated for an angle of 60 and the fade values for

an elevation angle of 80 provided in Table 1;

– linearly interpolate between the values in Table 1 and a value of zero at 90.

4 Rec. ITU-R P.681-11

FIGURE 1

Fading at 1.5 GHz due to roadside shadowing versus path elevation angle

P.0681-01

0

4

6

8

10

12

14

16

18

20

22

24

26

28

30

2

Fad

e ex

ceed

ed (

dB)

10 15 20 25 30 35 40 45 50 55 60

1%

2%

5%

10%

20%

30%

50%

Path elevation angle (degrees)

TABLE 1

Fades exceeded (dB) at 80 elevation

p

(%)

Tree-shadowed

1.6 GHz 2.6 GHz

1 4.1 9.0

5 2.0 5.2

10 1.5 3.8

15 1.4 3.2

20 1.3 2.8

30 1.2 2.5

4.1.1.2 Application of roadside shadowing model to non-geostationary (non-GSO) and

mobile-satellite systems

The prediction method above was derived for, and is applied to, LMSS geometries where the

elevation angle remains constant. For non-GSO systems, where the elevation angle is varying, the

link availability can be calculated in the following way:

a) calculate the percentage of time for each elevation angle (or elevation angle range) under

which the terminal will see the spacecraft;

b) for a given propagation margin (ordinate of Fig. 1), find the percentage of unavailability for

each elevation angle;

Rec. ITU-R P.681-11 5

c) for each elevation angle, multiply the results of step a) and b) and divide by 100, giving the

percentage of unavailability of the system at this elevation;

d) add up all unavailability values obtained in step c) to arrive at the total system unavailability.

If the antenna used at the mobile terminal does not have an isotropic pattern, the antenna gain at each

elevation angle has to be subtracted from the fade margin in step b) above.

In the case of multi-visibility satellite constellations employing satellite path diversity (i.e. switching

to the least impaired path), an approximate calculation can be made assuming that the spacecraft with

the highest elevation angle is being used.

4.1.2 Fade duration distribution model

Optimal design of LMSS receivers depends on knowledge of the statistics associated with fade

durations, which can be represented in units of travelled distance (m) or (s). Fade duration

measurements have given rise to the following empirical model which is valid for distance fade

duration dd 0.02 m.

2

)ln(–)ln(erf–1

2

1)|(

ddAAddFDP q (6)

where )|( qAAddFDP represents the probability that the distance fade duration, FD, exceeds the

distance, dd (m), under the condition that the attenuation, A, exceeds Aq. The designation “erf ”

represents the error function, is the standard deviation of ln(dd ), and ln() is the mean value of

ln(dd ). The left-hand side of equation (6) was estimated by computing the percentage number of

“duration events” that exceed dd relative to the total number of events for which A Aq in data

obtained from measurements in the United States of America and Australia. The best fit regression

values obtained from these measurements are 0.22 and 1.215.

Figure 2 contains a plot of P, expressed as a percentage, p, versus dd for a 5 dB threshold.

The model given by equation (6) is based on measurements at an elevation angle of 51 and is

applicable for moderate to severe shadowing (percentage of optical shadowing between 55% and

90%). Tests at 30 and 60 have demonstrated a moderate dependence on elevation angle: the smaller

the elevation angle, the larger is the fade duration for a fixed percentage. For example, the 30 fade

duration showed approximately twice that for the 60 fade duration at the same percentage level.

4.1.3 Non-fade duration distribution model

A non-fade duration event of distance duration, dd, is defined as the distance over which the fade

levels are smaller than a specified fade threshold. The non-fade duration model is given by:

–)()|( ddAAddNFDp q (7)

where )|( qAAddNFDp is the percentage probability that a continuous non-fade distance, NFD,

exceeds the distance, dd, given that the fade is smaller than the threshold, Aq. Table 2 contains the

values of and for roads that exhibit moderate and extreme shadowing i.e. the percentage of optical

shadowing of between 55% and 75% and between 75% and 90% respectively. A 5 dB fade threshold

is used for Aq.

6 Rec. ITU-R P.681-11

FIGURE 2

Best fit cumulative fade distribution for roadside tree

shadowing with a 5 dB threshold

P.0681-02

1

2

5

2

5

102

10

2 5 2 5 2 5

1 1010– 110– 2

Per

cent

age

of f

ade

dura

tion

> a

bsc

issa

Fade duration (m)

TABLE 2

Non-fade duration regression values for a 5 dB fade threshold

at a path elevation angle of 51°

Shadowing level

Moderate 20.54 0.58

Extreme 11.71 0.8371

4.2 Roadside building-shadowing model

Shadowing by roadside buildings in an urban area can be modelled by assuming a Rayleigh

distribution of building heights. Figure 3 shows the geometry.

Rec. ITU-R P.681-11 7

FIGURE 3

Geometry of roadside building shadowing model

P.0681-03

dm

Mobileheight, hm

Slope distance to Fresnel clearance point, d r

Buildingheight, hb

Height of rayabove groundat front ofbuildings, h1

Direction of road

Elevation,

Azimuth,

The percentage probability of blockage due to the buildings is given by:

2122

21 for2)(exp100 / hhhhhp b (8)

where:

h1 : height of the ray above ground at the building frontage, given by:

)sintan( /1 mm dhh (8a)

h2 : Fresnel clearance distance required above buildings, given by:

5.02 )( rf dCh (8b)

hb : the most common (modal) building height

hm : height of mobile above ground

: elevation angle of the ray to the satellite above horizontal

: azimuth angle of the ray relative to street direction

dm : distance of the mobile from the front of the buildings

dr : slope distance from the mobile to the position along the ray vertically above

building front, given by:

)cossin(/ mr dd (8c)

Cf : required clearance as a fraction of the first Fresnel zone

: wavelength

and where h1, h2, hb, hm, dm, dr and are in self-consistent units, and h1 h2.

Note that equations (8a), (8b) and (8c) are valid for 0 90 and for 0 180. The actual

limiting values should not be used.

Figure 4 shows examples of roadside building shadowing computed using the above expressions for:

hb 15 m

hm 1.5 m

dm 17.5 m

8 Rec. ITU-R P.681-11

Frequency 1.6 GHz.

FIGURE 4

Examples of roadside building shadowing

(see text for parameter values)

P.0681-04

0 10 20 30 40 50 60 70 800

20

40

60

80

100

Azimuth = 90°

Azimuth = 45°

Elevation angle (degrees)

Per

cen

tag

e p

rob

abil

ity

of

blo

ckag

e

Blockage assumed to occur at 0.7 Fresnel zone clearanceBlockage assumed to occur at zero Fresnel zone clearance

In Fig. 4 the dashed lines apply when blocking is considered to exist if the ray has a clearance less

than 0.7 of the first Fresnel Zone vertically above the building front. The solid lines apply when

blocking is considered to exist only when there is no line-of-sight.

Although the model indicates no blockage at the highest path elevation angles, users should be aware

that occasional shadowing and blockage can occur from overpasses, overhanging standards,

branches, etc.

4.3 Special consideration of hand-held terminals (user blockage)

When using hand-held communication terminals, the operator’s head or body in the near-field of the

antenna causes the antenna pattern to change. For the case of non-low Earth orbit (non-LEO) satellite

systems (GSO, high Earth orbit (HEO), ICO), the user of the hand-held terminal is expected to be

cooperative, i.e. to position himself in such a way as to avoid blockage from both the head (or body)

and the environment. For LEO systems this assumption cannot be made. The influence of the head

(or body) can be evaluated by including the modified antenna pattern (which has to be measured) in

the link availability calculation as presented in § 4.1.1.2. Assuming that the azimuth angles under

which the satellite is seen are evenly distributed, an azimuth-averaged elevation pattern can be

applied. The small movements of the head or hand which lead to small variations in apparent elevation

angle can also be averaged.

Rec. ITU-R P.681-11 9

Relating to this effect, a field experiment was performed in Japan. Figure 5a shows the geometry of

a human head and an antenna in the experiment. The satellite elevation angle is 32 and the satellite

signal frequency is 1.5 GHz. The antenna gain is 1 dBi and the length is 10 cm. Figure 5b shows the

variation of relative signal level versus azimuth angle in Fig. 5a. It can be seen from Fig. 5b that

the maximum reduction in signal level due to user blockage is about 6 dB when the equipment is in

the shadow region of the human head.

The results presented in Fig. 5b are intended to be illustrative only, since the data correspond to a

single elevation angle and antenna pattern, and no account is taken of potential specular reflection

effects, which may play a significant role in a hand-held environment where little directivity is

provided.

Propagation data related to signal entry loss for reception within buildings and vehicles, of particular

interest for hand-held terminals, may be found in Recommendation ITU-R P.679.

4.4 Modelling building blockage effects using street masking functions (MKF)

Building blockage effects can also be quantified using street MKFs indicating the azimuths and

elevations for which a link can or cannot be completed. Functions of this type have often been

obtained by means of photogrametric studies or ray-tracing. The MKF concept can be applied to

simplified scenarios to produce a limited number of MKFs and hence, making it possible to

produce fast, approximate assessments of the combined availability in different multi-satellite

configurations.

A given urban area could be described, as a first approximation, by an average masking angle (MKA)

(degrees).

The MKA is defined as the satellite elevation for grazing incidence with building tops when the link

is perpendicular to the street or in mathematical terms:

2/arctan

w

hMKA degrees (9)

where:

h : average building height

w : average street width.

Further, an urban scenario with a given MKA can be assumed to be made up of a combination of a

small number of typical configurations (basic/constitutive scenarios), namely, street canyons (scy),

street crossings (scr), T-junctions (T-j) and single walls (sw), each with a given occurrence probability

(see Fig. 5). Similarly a path-mixture vector, ,M could be defined, stating, for a given built-up area,

the probabilities of encountering each of the constitutive scenarios M (wscy, wscr, wT-j, wsw), with

1iw . Input data to this model, i.e., MKA, can be obtained by observation of the environment or

from city maps.

10 Rec. ITU-R P.681-11

FIGURE 5

Basic/constitutive scenarios describing a given urban area

P.0681-05

l1 l1

w2

l1

l1

w2

l1

l1

w1

l2

w1

w1

l2

l2

a) b)

c) d)

w1

3

1

21

1

23

1

If availability probabilities are worked out for those four constitutive scenarios, the overall

availability could be roughly estimated as the weighted sum of the availabilities in each scenario:

swswT-jT-jscrscrscyscyT awawawawa (10)

The MKFs for these four basic scenarios have been constructed by means of simple geometry

assuming the user is in the middle of the scene (see Fig. 5). Considering a simple on-off, or line-of-

sight – non-line-of-sight, propagation model (as in § 4.2 for the zero Fresnel zone clearance case),

the MKFs of the four constitutive urban scenarios are presented in Fig. 6 where the ordinates indicate

elevation angles and the abscissas azimuths or, rather, street orientations, , with respect to the link.

The top half-plane indicates positive azimuths and the bottom half-plane corresponds to negative

azimuths. A MKF indicates the regions in the celestial hemisphere where a link can be completed

(non-shaded) or not (shaded areas). The contours delimiting the “forbidden” zones in the MKFs are

defined by segments and points. The most relevant ones are illustrated in Fig. 6 and given by the

following equations:

1

tan

1

2/tanθ:

2

21 w

hSA (11a)

2/tanθ;º90: 1

w

hP AAA (11b)

1

tan

1

2/tanθ:

2

211

1

whSB (11c)

Rec. ITU-R P.681-11 11

1

)º90(tan

1

2/tanθ:

2

211

2

whSB (11d)

1

tan

1

2/tanθ;tan:

2

211

22

11

B

BBw

hw

wP (11e)

FIGURE 6

MKFs of a) a street canyon, b) a single wall,

c) a street crossing and d) a T-junction

P.0681-06

80

60

40

20

0

20

40

60

80

160–160

180–180

140–140

120–120

100–100

80–80

40–40

20–20

00

160–160

180–180

140–140

120–120

100–10080

60–60

40–40

20–20

00 –80

80

60

40

20

0

20

40

60

80

160–160

180–180

140–140

120–120

100–100

60–60

40–40

20–20

00

80–80

80

60

40

20

0

20

40

60

80

60–60

80

60

40

20

0

20

40

60

80

160

–160

180

–180

140

–140

120

–120

100

–100

60

–60

40

–40

20

–20

0

0

80–80

h = 20

w1 = 20

w2 = 20

MKA

SA

PA

PB

SB 2

SB1

Ele

vat

ion

ang

le (

deg

rees

)

Azimuth (degrees)

Ele

vati

on

ang

le (

deg

rees

)

Azimuth (degrees)

Ele

vat

ion

ang

le (

deg

rees

)

Azimuth (degrees)

Ele

vati

on

ang

le (

deg

rees

)

Azimuth (degrees)a) b)

c) d)

The availability for a particular basic scenario and a given geostationary (GSO) satellite can be

computed by considering all possible street orientations, , with respect to the user-satellite link. In

Fig. 7 the position of a GSO satellite with respect to a T-junction is indicated. For the case illustrated

in the Figure all possible orientations can be described by sweeping through all points in line A-B

corresponding to a constant elevation angle and all possible street orientations. The availability is the

fraction of the straight line A-B in the non-shaded part of the MKF. Similarly, a non-GSO orbit

12 Rec. ITU-R P.681-11

trajectory can be drawn on an MKF. The overall availability can be computed in this case by

considering all possible street orientations with respect to all possible user-satellite link directions.

FIGURE 7

Calculation of the availability for a T-junction and a GSO satellite

P.0681-07

80

60

40

20

0

20

40

60

80

160–160

180–180

140–140

120–120

100–100

60–60

40–40

20–20

00

h = 20

w1 = 20

w2 = 20

80–80

B

B

A

A

Azimuth (degrees)

MKF, T-junction

Azimuthsweep,

Position of satellite

Azi

mu

th s

wee

p

Azi

mu

th s

wee

p

Ele

vatio

n(d

egre

es)

Starting point of azimuth sweep

Position of satellite

Azimuth sweep

Unavailability regionUnavailability region

Unavailability region

Azimuth sweep

MKA

5 Multipath models for clear line-of-sight conditions

In many cases the mobile terminal has a clear line-of-sight (negligible shadowing) to the mobile

satellite. Degradation to the signal can still occur under these circumstances, due to terrain-induced

multipath. The mobile terminal receives a phasor summation of the direct line-of-sight signal and

several multipath signals. These multipath signals may add constructively or destructively to result

in signal enhancement or fade. The multipath signal characteristics depend on the scattering cross-

sections of the multipath reflectors, their number, the distances to the receiving antenna, the field

polarizations, and receiving antenna gain pattern.

The multipath degradation models introduced in the following sections are based on measurements

made using an antenna with the following characteristics:

– omnidirectional in azimuth;

– gain variation between 15 and 75 elevation less than 3 dB;

– below the horizon (negative elevation angles) the antenna gain was reduced by at least 10 dB.

Rec. ITU-R P.681-11 13

FIGURE 8

a) Geometry of a human head and an antenna;

b) Fading at 1.5 GHz due to roadside shadowing versus path elevation angle

P.0681-08

5 cm

d

177 cm

32°

0 90 180 270 360– 6

– 4

– 2

0

2

d = –17 cm

d = –9 cm

d = +3 cm

Satellite signal

Humanhead

Top view

Antenna

Antenna(quadrifilar helix)

Side view

Ground

Humanhead

Elevation angle = 32°

Azimuth angle, (degrees)

Rel

ativ

e si

gnal

lev

el (

dB)

Average receivedlevel in line-of-sightcondition

Satellite Satellite

14 Rec. ITU-R P.681-11

5.1 Multipath in a mountain environment

The distribution of fade depths due to multipath in mountainous terrain is modelled by:

bAap – (12)

for:

%10%1 p

where:

p : percentage of distance over which the fade is exceeded

A : fade exceeded (dB).

The curve fit parameters, a and b, are shown in Table 3 for 1.5 GHz and 870 MHz. Note that the

above model is valid when the effect of shadowing is negligible.

TABLE 3

Parameters for best fit cumulative fade distribution

for multipath in mountainous terrain

Frequency

(GHz)

Elevation 30 Elevation 45

a b Range

(dB) a b

Range

(dB)

0.87 34.52 1.855 2-7 31.64 2.464 2-4

1.5 33.19 1.710 2-8 39.95 2.321 2-5

Figure 9 contains curves of the cumulative fade distributions for path elevation angles of 30 and 45

at 1.5 GHz and 870 MHz.

5.2 Multipath in a roadside tree environment

Experiments conducted along tree-lined roads in the United States of America have shown that

multipath fading is relatively insensitive to path elevation over the range of 30 to 60. The measured

data have given rise to the following model:

p u exp (– v A) (13)

for:

1% p 50%

where:

p : percentage of distance over which the fade is exceeded

A : fade exceeded (dB).

Note that the above model assumes negligible shadowing. The curve fit parameters, u and v, are

shown in Table 4.

Rec. ITU-R P.681-11 15

FIGURE 9

Best fit cumulative fade distributions for multipath fading in mountainous terrain

P.0681-09

Fade depth (dB)

Per

cen

tag

e of

dis

tanc

e fa

de >

ab

scis

sa

Cu rv es A: 8 70 M Hz , 4 5 ° B: 1 .5 G h z , 4 5 °Cu rv es C: 8 70 M Hz , 3 0 °Cu rv es D : 1 . 5 G Hz , 3 0 °Cu rv es

A B C D

0 1 2 3 4 5 6 7 8 9 10

2

5

2

1

10

TABLE 4

Parameters for best exponential fit cumulative fade distributions

for multipath for tree-lined roads

Frequency

(GHz) u v

Fade range

(dB)

0.870 125.6 1.116 1-4.5

1.5 127.7 0.8573 1-6

16 Rec. ITU-R P.681-11

Figure 10 contains curves of the cumulative fade distributions for 1.5 GHz and 870 MHz. Enhanced

fading due to multipath can occur at lower elevation angles (5 to 30) where forward scattering from

relatively smooth rolling terrain can be received from larger distances.

FIGURE 10

Best fit cumulative fade distributions for multipath fading on tree-lined roads

P.0681-10

A B

1

10

2

5

2

5

102

0 1 2 3 4 5 6 7 8 9 10

Per

cen

tage

of

dis

tan

ce f

ade

> a

bsci

ssa

Fade depth (dB)

Curves A: 870 MHzB: 1.5 GHzCurves

6 Statistical model for mixed propagation conditions

In §§ 4.1 and 5, models for specific conditions, that is, roadside shadowing conditions and clear

line-of-sight conditions in a mountain environment and a roadside tree environment are given.

In actual LMSS propagation environments such as rural, wooded, urban and suburban areas,

a mixture of different propagation conditions can occur. The cumulative distribution function (CDF)

of signal levels in such mixed conditions can be calculated based on the following enhanced 2-state

model which is composed of a GOOD state, including slightly shadowed conditions, and a BAD state,

including more severe shadowed conditions (referred as “statistical model” hereafter). Based on the

same analytical assumptions, time/space series of the power signal level complex envelope can be

stochastically generated (referred as “generative model” hereafter). Sections 6.1 and 6.2 provide step-

by-step methods to implement respectively the statistical and the generative models. Both models are

valid for narrow-band LMSS where the frequency response of the channel affects in the same way all

the frequencies within the bandwidth of the signal (frequency non-selective channels).

Rec. ITU-R P.681-11 17

The long-term variations in the received signal may be described by a semi-Markov chain including

the two distinct states, GOOD and BAD (see Fig. 11). The duration of each state is considered to be

log-normally distributed. The signal in the Good and Bad states follows a Loo distribution. The Loo

distribution considers that the received signal is the sum of two components: the direct path signal

and the diffuse multipath. The average direct path amplitude is considered to be normally distributed

and the diffuse multipath component follows a Rayleigh distribution. The standard deviation of the

direct path amplitude and the multipath power are linearly connected to the average direct path

amplitude.

FIGURE 11

2-State Semi-Markov chain approach

P.0681-11

Badstate

Goodstate

Pdf durationof bad state

Pdf durationof Good state

For the stochastic synthesis of the channel complex envelope, a fixed correlation length for the direct

path amplitude should be considered and a fixed Doppler spectrum should be considered for the

diffuse multipath component. Between two successive events (belonging necessarily to different

states), a given transition length must be considered where the diffuse multipath component power

increases/decreases linearly. These transitions should be neglected for the statistical prediction of the

channel complex envelope.

The main characteristics of the model are:

1) The model assumes two states: Good and Bad not necessarily matching with

line-of-sight and non-line-of-sight condition.

2) The duration of each state is characterized by a lognormal distribution:

𝑝𝑙𝑜𝑔𝑛𝑜𝑟𝑚𝑎𝑙(𝑥) =1

σ𝑖𝑥√π𝑒𝑥𝑝 [

(𝑙𝑛𝑥−μ𝑖)2

2σi2 ] (14)

where:

i = G for Good states

i = B for Bad states

µG and σG: mean and standard deviation for Good state

µB and σB: mean and standard deviation for Bad state

3) The fading within each state is described by a Loo distribution, where the Loo triplet

parameters are not fixed:

Fading~Loo(MAi, ΣAi, MPi),

18 Rec. ITU-R P.681-11

where:

i = G for Good states

i = B for Bad states

MAi : mean of the direct signal

ΣAi : standard deviation of the direct signal

MPi : mean of the multipath

with:

MAi = normal( μ𝑀𝐴 , σMA

)

ΣAi = g1iMAi + g2i

MPi= h1iMAi + h2i

The Loo probability density function is:

daxa

IaxMa

a

xxp

iiAi

Ai

iAi

Loo

20

02

22

2

210

2 22

))(log20(exp

1

2

686.8)( (15)

where

a : direct signal amplitude

2σi2 : multipath mean received power, MPi=10log (2σi

2) dB

3) The transition length Ltrans,i between a GOOD and BAD event depends on the MA,i values

difference MA,i = |MA,i GOOD – MA,i BAD |:

Ltrans,i = f1 MA,i + f2 (16)

In order not to consider unrealistic values for MA in GOOD and BAD states, restricted probability

ranges must be considered:

• 5% – 95% for the GOOD state

• [pB,min , pB,max] for the BAD state.

In order to consider realistic values for the GOOD and BAD state events duration, minimum possible

event lengths must be considered:

• durminG for the GOOD state

• durminB for the BAD state.

The following input parameters should be used for the statistical and the generative models.

Rec. ITU-R P.681-11 19

TABLE 5

Model parameters

Parameter Description

(µ,)G,B Mean and standard deviation of the log-normal law assumed for events duration

(m)

durminG,B Minimum possible events duration (m)

(μ𝑀𝐴 GB, σ𝑀𝐴 GB) Parameters of the MA G,B distribution (MA being the average value of the direct

path amplitude A over one event) (dB)

MP = h1G,BMA+h2G,B Multipath power, MPG,B, (one 1st order polynomial for each state), (dB)

∑AG,B = g1G,BMA+g2G,B Standard deviation of A, ∑𝐴 𝐺,𝐵 (one 1st order polynomial for each state)

LcorrG,B* Direct path amplitude correlation distance (m)

f1ΔMA+f2 Transition length, Ltrans (one single 1st order polynomial), (m)

[pB,min , pB,max] Probability range to consider for the MA B distribution

Remark: G stands for the GOOD state and B stands for the BAD state.

* Only for generative modelling.

6.1 Prediction of fading statistics for a single satellite link

The following procedure provides an estimation of overall fading statistics of the LMSS propagation

link for frequencies up to 30 GHz with elevation angles from 20° to 90°. However, the suggested

parameter values given here limit the applicable frequency range of 1.5 GHz to 20 GHz. The receiving

antenna gain assumed here is about 5 dBi for frequencies below 5 GHz and 19 dBi for frequencies

above 10 GHz.

Remark: The statistical prediction method has been simplified with respect to the time series synthesis

method (§ 6.2) to provide an approximate value of the fading, Rice factor and total power statistics.

For better accuracy, statistics must be computed from time series synthesised over 100 km.

Inputs:

– frequency (Hz);

– environment;

– elevation angle.

Step 0: Determine the (µ,)G,B , ( μ𝑀𝐴 , σ𝑀𝐴

)G,B, (g1,g2)G,B, (h1,h2)G,B, (durmin)G,B ,(f1,f2), pB,min and pB,max from the

input parameters table provided in Annex 2. Consider the table corresponding to the closer elevation

angle and frequency to the input values.

Step 1: Calculate the average duration of GOOD and BAD states, respectively <dur>G and <dur>B,

and the average transition length, <dur>T:

⟨𝑑𝑢𝑟⟩𝐺,𝐵 = 𝑒𝑥𝑝 (μ𝐺,𝐵 +σ𝐺,𝐵

2

2)

1−𝑒𝑟𝑓(𝑙𝑜𝑔𝑑𝑢𝑟𝑚𝑖𝑛,𝐵,𝐺−(μ𝐺,𝐵+σ𝐺,𝐵

2 )

σ√2)

1−𝑒𝑟𝑓(𝑙𝑜𝑔𝑑𝑢𝑟𝑚𝑖𝑛,𝐵,𝐺−μ𝐺,𝐵

σ√2)

(17a)

⟨𝑑𝑢𝑟⟩𝑇 = 𝑓1 × (𝜇𝑀𝐴,𝐺 − μ𝑀𝐴,𝐵 − σ𝑀𝐴,𝐵2 ×

𝑝𝑁(𝑀𝐴,𝑚𝑖𝑛;μ𝑀𝐴,𝐵,σ𝑀𝐴,𝐵)−𝑝𝑁(𝑀𝐴,𝑚𝑎𝑥;μ𝑀𝐴,𝐵,σ𝑀𝐴,𝐵)

𝐹𝑁(𝑀𝐴,𝑚𝑎𝑥;μ𝑀𝐴,𝐵,)−𝐹𝑁(𝑀𝐴,𝑚𝑖𝑛;μ𝑀𝐴,𝐵,σ𝑀𝐴,𝐵)) + 𝑓2 (17b)

Where

20 Rec. ITU-R P.681-11

pN(x; ,) and FN(x; ,) are respectively the probability density function and the cumulative

distribution function of a normal distribution with mean and standard deviation as defined in

Recommendation ITU-R P.1057.

𝑀𝐴,𝑚𝑖𝑛,𝐵 = μ𝑀𝐴𝐵 + √2σ𝑀𝐴,𝐵𝑒𝑟𝑓−1(2𝑝𝐵,𝑚𝑖𝑛 − 1) (18a)

𝑀𝐴,𝑚𝑎𝑥,𝐵 = μ𝑀𝐴𝐵 + √2σ𝑀𝐴,𝐵𝑒𝑟𝑓−1(2𝑝𝐵,𝑚𝑎𝑥 − 1) (18b)

Step 2: Calculate the probability of GOOD and BAD states pG and pB:

𝑝𝐺 =⟨𝑑𝑢𝑟⟩𝐺+⟨𝑑𝑢𝑟⟩𝑇

⟨𝑑𝑢𝑟⟩𝐺+⟨𝑑𝑢𝑟⟩𝐵+2⟨𝑑𝑢𝑟⟩𝑇 (19a)

𝑝𝐵 =⟨𝑑𝑢𝑟⟩𝐵+⟨𝑑𝑢𝑟⟩𝑇

⟨𝑑𝑢𝑟⟩𝐺+⟨𝑑𝑢𝑟⟩𝐵+2⟨𝑑𝑢𝑟⟩𝑇 (19b)

Step 3: Calculate 𝑃(𝑥 ≤ 𝑥0|𝐺𝑂𝑂𝐷) and 𝑃(𝑥 ≤ 𝑥0|𝐵𝐴𝐷) the cumulative distribution of signal level

x in GOOD and BAD states as follows:

𝑃(𝑥 ≤ 𝑥0|𝑠𝑡𝑎𝑡𝑒)

=2.7647

σ𝑀𝐴(𝐹𝑁 (𝑀𝐴,𝑚𝑎𝑥; μ𝑀𝐴

, σ𝑀𝐴) − 𝐹𝑁 (𝑀𝐴,𝑚𝑖𝑛; μ𝑀𝐴

, σ𝑀𝐴))

∫ ∫ ∫𝑥

𝑎(𝑔1𝑀𝐴 + 𝑔2)10ℎ1𝑀𝐴+ℎ2

10

𝑎𝑚𝑎𝑥

𝑎𝑚𝑖𝑛

𝑥0

0

𝑀𝐴,𝑚𝑎𝑥

𝑀𝐴,𝑚𝑖𝑛

× 𝑒𝑥𝑝 (−(𝑀𝐴 − μ𝑀𝐴

)2

2σ𝑀𝐴

2 −(20 log10 𝑎 − 𝑀𝐴)2

2(𝑔1𝑀𝐴 + 𝑔2)2−

𝑥2 + 𝑎2

10ℎ1𝑀𝐴+ℎ2

10

) 𝐼0 (2𝑎𝑥

10ℎ1𝑀𝐴+ℎ2

10

) 𝑑𝑎 𝑑𝑥 𝑑𝑀𝐴

(20a)

where

Parameter GOOD state BAD state

𝑀𝐴,𝑚𝑖𝑛 μ𝑀𝐴,𝐺 − 1.645 × σ𝑀𝐴,𝐺 𝑀𝐴,𝑚𝑖𝑛,𝐵

𝑀𝐴,𝑚𝑎𝑥 μ𝑀𝐴,𝐺 + 1.645 × σ𝑀𝐴,𝐺 𝑀𝐴,𝑚𝑎𝑥,𝐵

𝑎𝑚𝑖𝑛 10

(1−3𝑔1)𝑀𝐴−3𝑔220

10(1+3𝑔1)𝑀𝐴+3𝑔2

20 𝑎𝑚𝑎𝑥

Please note that σ𝑀𝐴may be equal to zero (as for example in the good states of rural and suburban

environment for f = 10 – 20 GHz). In such condition, MA is not randomly distributed which changes

the expression of the CDF (no integration other than Ma). Then, the cumulative distribution become

(with: 𝑀𝐴 = μ𝑀𝐴 here).

𝑃(𝑥 ≤ 𝑥0|𝑠𝑡𝑎𝑡𝑒) =2×8.686

√2π∫ ∫

𝑥

𝑎(𝑔1𝑀𝐴+𝑔2)10ℎ1𝑀𝐴+ℎ2

10

× 𝑒𝑥𝑝 (−( 20log10𝑎−𝑀𝐴)2

2(𝑔1𝑀𝐴+𝑔2)2 −𝑥2+𝑎2

10ℎ1𝑀𝐴+ℎ2

10

) 𝐼0 (2𝑎𝑥

10ℎ1𝑀𝐴+ℎ2

10

) 𝑑𝑎𝑎𝑚𝑎𝑥

𝑎𝑚𝑖𝑛𝑑𝑥

𝑥0

0 (20b)

Step 4: Calculate 𝑃(𝑥 ≤ 𝑥0) the cumulative distribution of signal level x as follows:

𝑃(𝑥 ≤ 𝑥0) = 𝑝𝐺 × 𝑃(𝑥 ≤ 𝑥0|𝐺𝑂𝑂𝐷) + 𝑝𝐵 × 𝑃(𝑥 ≤ 𝑥0|𝐵𝐴𝐷) (21)

Step 5: Calculate 𝑃(𝐾 ≤ 𝐾0|𝐺𝑂𝑂𝐷) and 𝑃(𝐾 ≤ 𝐾0|𝐵𝐴𝐷) the cumulative distribution of the Rice

factor (dB) K in GOOD and BAD states, as follows:

Rec. ITU-R P.681-11 21

If σ𝑀𝐴≠ 0

𝑃(𝐾 ≤ 𝐾0|𝑠𝑡𝑎𝑡𝑒) =

∫ 𝑒𝑥𝑝 (−(𝑀𝐴 − μ𝑀𝐴

)2

2σ𝑀𝐴

2 ) [1 + 𝑒𝑟𝑓 (𝐾0 − ((1 − ℎ1)𝑀𝐴 − ℎ2)

(𝑔1𝑀𝐴 + 𝑔

2)√2

)] 𝑑𝑀𝐴𝑀𝐴,𝑚𝑎𝑥

𝑀𝐴,𝑚𝑖𝑛

σ𝑀𝐴(𝐹𝑁 (𝑀𝐴,𝑚𝑎𝑥; 𝜇

𝑀𝐴, σ𝑀𝐴

) − 𝐹𝑁 (𝑀𝐴,𝑚𝑖𝑛; μ𝑀𝐴

, σ𝑀𝐴)) 2√2𝜋

(22a)

If σ𝑀𝐴= 0, then

𝑃(𝐾 ≤ 𝐾0|𝑠𝑡𝑎𝑡𝑒) =1+𝑒𝑟𝑓(

𝐾0−((1−ℎ1)𝑀𝐴−ℎ2)

(𝑔1𝑀𝐴+𝑔2)√2)

2 (22b)

Step 6: Calculate 𝑃(𝐾 ≤ 𝐾0) the cumulative distribution of the Rice factor K, as follows:

𝑃(𝐾 ≤ 𝐾0) = 𝑝𝐺 × 𝑃(𝐾 ≤ 𝐾0|𝐺𝑂𝑂𝐷) + 𝑝𝐵 × 𝑃(𝐾 ≤ 𝐾0|𝐵𝐴𝐷) (23)

Step 7: Calculate 𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝐺𝑂𝑂𝐷) and 𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝐵𝐴𝐷) the cumulative distribution of the total

power pt (direct path power plus diffuse multipath power) in GOOD and BAD states as follows:

For h1 0:

If 10𝑙𝑜𝑔𝑝𝑡,0−ℎ2

ℎ1< 𝑀𝐴,𝑚𝑖𝑛, 𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝑠𝑡𝑎𝑡𝑒) = 0 (24a)

If 10𝑙𝑜𝑔𝑝𝑡,0−ℎ2

ℎ1𝑀𝐴,𝑚𝑖𝑛 and σ𝑀𝐴

≠ 0

𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝑠𝑡𝑎𝑡𝑒)

=

∫ 𝑒𝑥𝑝 (−(𝑀𝐴 − μ𝑀𝐴

)2

2σ𝑀𝐴

2 ) [1 + 𝑒𝑟𝑓 (10𝑙𝑜𝑔 (𝑝𝑡,0 − 10

ℎ1𝑀𝐴+ℎ2

10 ) − 𝑀𝐴

(𝑔1𝑀𝐴 + 𝑔

2)√2

)] 𝑑𝑀𝐴

𝑚𝑖𝑛{𝑀𝐴,𝑚𝑎𝑥;10𝑙𝑜𝑔𝑝𝑡,0−ℎ2

ℎ1}

𝑀𝐴,𝑚𝑖𝑛

σ𝑀𝐴(𝐹𝑁 (𝑀𝐴,𝑚𝑎𝑥; μ

𝑀𝐴, σ𝑀𝐴

) − 𝐹𝑁 (𝑀𝐴,𝑚𝑖𝑛; μ𝑀𝐴

, σ𝑀𝐴)) 2√2π

(24b)

For h1 < 0:

If 10𝑙𝑜𝑔𝑝𝑡,0−ℎ2

ℎ1> 𝑀𝐴,𝑚𝑎𝑥, 𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝑠𝑡𝑎𝑡𝑒) = 0 (24c)

If 10𝑙𝑜𝑔𝑝𝑡,0−ℎ2

ℎ1𝑀𝐴,𝑚𝑎𝑥 and σ𝑀𝐴

≠ 0,

𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝑠𝑡𝑎𝑡𝑒) =

∫ 𝑒𝑥𝑝(−(𝑀𝐴−μ𝑀𝐴

)2

2σ𝑀𝐴2 )[1+𝑒𝑟𝑓(

10𝑙𝑜𝑔(𝑝𝑡,0−10

ℎ1𝑀𝐴+ℎ2

10 )−𝑀𝐴

(𝑔1𝑀𝐴+𝑔2)√2)]𝑑𝑀𝐴

𝑀𝐴,𝑚𝑎𝑥

𝑚𝑎𝑥{𝑀𝐴,𝑚𝑖𝑛;10𝑙𝑜𝑔𝑝𝑡,0−ℎ2

ℎ1}

σ𝑀𝐴(𝐹𝑁(𝑀𝐴,𝑚𝑎𝑥;μ𝑀𝐴

,σ𝑀𝐴)−𝐹𝑁(𝑀𝐴,𝑚𝑖𝑛;μ𝑀𝐴

,σ𝑀𝐴))2√2π

(24d)

If σ𝑀𝐴= 0, then

𝑃(𝑝𝑡 ≤ 𝑝𝑡,0|𝑠𝑡𝑎𝑡𝑒) =

1+𝑒𝑟𝑓(10𝑙𝑜𝑔(𝑝𝑡,0−10

ℎ1𝑀𝐴+ℎ2

10 )−𝑀𝐴

(𝑔1𝑀𝐴+𝑔2)√2)

2 (24e)

22 Rec. ITU-R P.681-11

Step 8: Calculate 𝑃(𝑝𝑡 ≤ 𝑝𝑡,0) the cumulative distribution of the total power pt as follows:

)()()( 0,0,0, BADttBGOODttGtt ppPpppPpppP

(25)

Figures 12, 13 and 14 shows calculated examples of CDFs, for urban and suburban parameters

(Europe) at 30 and 60° elevation angle at frequencies between 1.5 and 3 GHz.

FIGURE 12

Calculated examples of fading depth in urban and suburban areas at elevation angles of 30° and 60°

(Europe; 1.5-3 GHz; antenna gain < 5 dBi)

P. 20681-1

1

– 30 0

20 log ( ) x0 (dB)

Suburban – 30°

– 25

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Suburban – 60°

Urban – 30°

Urban – 60°

Px

x(

<

) 0

– 20 – 15 – 10 – 50

Rec. ITU-R P.681-11 23

FIGURE 13

Calculated examples of fading Rice factor in urban and suburban areas at elevation angles of 30° and 60°

(Europe; 1.5-3 GHz; antenna gain < 5 dBi)

P. 30681-1

1

– 10 5 10 15

K0 (dB)

Suburban – 30°

– 5 0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Suburban – 60°

Urban – 30°

Urban – 60°

P

KK

(<

)

0

FIGURE 14

Calculated examples of fading total power in urban and suburban areas at elevation angles of 30° and 60°

(Europe; 1.5-3 GHz; antenna gain < 5 dBi)

P. 40681-1

1

0

20 log ( ) pt, 0

(dB)

Suburban – 30°

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Suburban – 60°

Urban – 30°

Urban – 60°

Pp

p(

<

tt

),

0

– 20 – 15 – 10 – 5

24 Rec. ITU-R P.681-11

6.2 Time series synthesis of fading complex envelope

Performance estimation of LMSS receivers requires stochastic synthesis of realistic time series of the

channel complex envelope. The semi-Markov enhanced 2-state model should be used to simulate the

LMSS time-variations of the channel for a single GSO satellite.

Figure 15 contains the simulator block diagram to generate time/space series of the received power

envelope.

FIGURE 15

Simulator block diagram

P. 50681-1

fVm

Ts

Selectmodelparam

Statesseries

Loo parametersand

transition lengths

Direct path andmultipath

components

Total Lootime seriesgeneration

env

The step by step generation of the power complex envelope time series is as follows:

Inputs:

– frequency f (Hz);

– elevation angle (°);

– azimuth/route orientation (°);

– environment;

– sampling time Ts (s);

– mobile speed vm (m.s-1).

Step 0: Selection of the model parameters (µ,)G,B , (μ𝑀𝐴, σ𝑀𝐴

)G,B, (g1,g2)G,B, (h1,h2)G,B, (durmin)G,B , (Lcorr)G,B,

f1, f2, confB,min, confB,max depending on the inputs. Consider the table corresponding to the closer elevation

angle and frequency to the input values. An example of model parameters is shown in Table 5.

Step 1: Generation of the State Series. A State Series consist of a series of Good events and Bad

events. The duration of each event is generated with a lognormal distribution. If a value lower than

durmin is drawn, new random draws should be performed until the value is higher than the parameter

value.

State_durationG~lognormal(µG, σG)

State_durationB~lognormal(µB, σB)

Figure 16 shows an example of state series, with Good and Bad events of different durations.

Rec. ITU-R P.681-11 25

FIGURE 16

Example of States Series

P.0681 6-1

Good

Bad

Distance(m)

0 1 000500 1 500 2 000 2 500

State series, semi-Markov

Step 2: Generation of the Loo parameters triplet (MA,ΣA,MP) for each state and the transition lengths

(Ltrans) between states. If a MA value out of the [μ𝑀𝐴,𝐺 − 1.645σ𝑀𝐴,𝐺; μ𝑀𝐴,𝐺 + 1.645σ𝑀𝐴,𝐺] range for

GOOD state and out of the [μ𝑀𝐴,𝐵 + √2σ𝑀𝐴,𝐵𝑒𝑟𝑓−1(2𝑝𝐵,𝑚𝑖𝑛 − 1) ; μ𝑀𝐴,𝐵 + √2σ𝑀𝐴,𝐵

𝑒𝑟𝑓−1(2𝑝𝐵,𝑚𝑎𝑥 − 1)] range

for BAD state is drawn, new random draws has to be performed until the value lies into this range.

TABLE 6

Good events Bad events

MAGi = Normal(μ𝑀𝐴,𝐺, σ𝑀𝐴,𝐺) MABi =Normal(μ𝑀𝐴,𝐵, σ𝑀𝐴𝐵)

ΣAG i = g1G*MAGi +g2G Σ AB i = g1B*MABi +g2B

MPGi = h1G*MAGi +h2G MPBi = h1B*MABi +h2B

Addition of the transition lengths Ltrans between states (see Fig. 17):

Ltrans= f1|MAi – MAi+1 |+ f2 (m) (26)

26 Rec. ITU-R P.681-11

FIGURE 17

Example of Loo parameters triplet for each states and insertion of transition lengths between states

P.0681 7-1

Good

Bad

State series

260 300280 320 340 360 380 400 420 440

State series

State + transitions

MA1

A1

MP1

MA2

A2

MP2

MA3

A3

MP3

r1 r2

Good

Distance (m)

Step 3: Generation of the Loo total time series

The complex signal variations can be produced using a Loo time series generator.

Its implementation is showed in Fig. 18. The parameters of the circuit will be updated for the

generations of time series in every state.

Inside a transition, the Loo parameters drawn for the GOOD and BAD states around the transition

are interpolated linearly (dB).

FIGURE 18

Loo time series generator

P.0681 8-1

-fmax

Doppler spread

+ +

fmax

j

= MP

10

( )nTs

Complexenvelope

A nT( )s ( )nTs

Low passfilter

H ZA( )

10A/20

G (0.1)

G (0.1)

G ( , )MA A

exp f nT(j2d s

)

(doppler shift of direct signal)

Rec. ITU-R P.681-11 27

The upper rail generates the multipath fast variations and the lower rail, the direct signal slow

variations.

In the upper rail two zero-mean and unit-standard deviation Gaussian series in quadrature are passed

through a unit-energy Doppler filter. After Doppler shaping, the resulting complex series is multiplied

by σ, with 2σ 2 being the mean square value of the multipath variations.

The lower rail performs the simulation of the direct signalʼs amplitude and phase variations.

In a first step, a Gaussian distribution with MA (dB) mean and ΣA (dB) standard deviation is generated.

In a second step, the series, in dB units, is converted to linear units.

In a third step, the phase variations in the direct signal are introduced. These are assumed to be

linearly-varying giving rise to a constant Doppler spectral line which depends on the relative mobile-

satellite velocity and the angle of arrival, azimuth and elevation, with respect to the mobile trajectory.

The Doppler spectral line frequency is given by:

fd = (fvm/c)cosφ·cosθ (27)

Fast variations are ruled by the Doppler spread mainly due to the terminalʼs motion. Depending on

the antenna pattern, a Jakes model must be used for generating the fast variations.

The Jakes filter is defined by:

(28)

where fm = vm×f/c and K is a normalisation parameter which ensures that the filtering does not change

the process power.

The direct signal's amplitude is subjected to variations slower than those due to multipath caused by

shadowing. In this implementation, the rate of change of the slow variations is characterized by the

correlation length, LcorrG for Good states or LcorrB for Bad states. The sampling distance of the

multipath being vmTs, the correlated shadowing time series are generated using the following

numerical low pass filter:

𝐻𝐴(𝑍) =√1−𝑠

2

1−𝑠𝑍−1 with 𝑠

= 𝑒𝑥𝑝 (−𝑣𝑚𝑇𝑠

𝐿𝑐𝑜𝑟𝑟) (29)

Figure 19 shows an example of generated time series (converted into space series).

28 Rec. ITU-R P.681-11

FIGURE 19

Example of generated space series

P. 90681-1

Distance (m)

10

0

– 10

– 20

– 30

– 40

dB

0 500 1 000 1 500 2 000 2 500

Total

Shadowing

7 Physical-statistical wideband model for mixed propagation conditions

In § 6, a statistical narrow-band model for LMSS in different environments is given. For broadband

LMSS with a multipath propagation channel where different frequencies within the signal bandwidth

are affected differently by the channel (frequency-selective channels), a generative model that

implements a linear transversal filter whose output is a sum of delayed, attenuated and phase shifted

versions of the input signal (wideband model) is more suitable. Definitions on terms related to

multipath propagation are found in Recommendation ITU-R P.1407.

The model is given for a situation where a satellite is transmitting from a known position to a receiver

on ground, where an elevation ε and an azimuth φ can be computed relative to the receiver heading

and position. The model can be applied for frequencies between 1 and 2 GHz and it is valid for

wideband systems with a bandwidth up to 100 MHz. The model is based on deterministic and

stochastic parameters and it is able to generate vectors that include complex envelope time-series of

direct signal and reflections, with corresponding path delay vectors. The parameters determining the

stochastic behaviour of the model are derived from measurements obtained on a given scenario. The

geometry of the model is based on a synthetic environment representation.

The channel model consists of a combination of the following parts (developed to support the

simulation of realistic propagation behaviour for many propagation scenarios of interest, and further

validated with empirical analyses based on measured data):

– Shadowing of the direct signal:

– house front module

– tree module

– light pole module

– Reflections module.

The structure of the model is illustrated in Fig. 20 including the following input, intermediate and

output time-variant signals:

vu(t): user speed

hdu(t): user heading

els(t): satellite elevation

azs(t): satellite azimuth

xu(t): user position in x-axis (y and z axis are considered constant)

Rec. ITU-R P.681-11 29

azu(t): user azimuth

yi(t): output signals, where each i is related to direct signal and reflectors.

The propagation mechanisms considered in the model and the synthetic environment are illustrated

in Fig. 21.

The model structure is valid for several scenarios: urban vehicle, urban pedestrian, suburban vehicle,

suburban pedestrian. The model was developed from measurements on urban and suburban scenarios

in and around Munich, Germany. A software with an implementation of the model is available at the

Radiocommunication Study Group 3 website. A complete description of the model implementation

and usage is provided in a related ITU-R Physical-Statistical Wideband LMSS Model Report

available on the ITU-R Study Group website.

FIGURE 20

Structure of the model

P.068120-

Motionmodel

Tree

Light poleReflector

model

hd (t)U

el (t)S

az (t)S

y (t)i

x (t)U

el (t)s

az (t)U

House front

Synthetic environmentV (t)U

FIGURE 21

Propagation mechanisms and synthetic environment

P.068121-

L So

Direction of

movement

Reflectors

50100

0

Housefront

Tree(diffraction and

attenuation)

Roofs and walls(diffraction)

Gaps inhouse front

Light pole(diffraction)

50

0

–80

–60

–40

–20

0

20

40

60

80

100

y

30 Rec. ITU-R P.681-11

7.1 Model input

For every input sample some values must be given for the model input:

– satellite elevation

– satellite azimuth

– user speed

– user heading.

Note that the maximum user speed is limited by the channel impulse response sampling frequency:

c

samp

f

fcv

2

0 (30)

where:

sampf : sampling frequency

cf : carrier frequency

0c : speed of light.

It is recommended a reasonable over-sampling factor such as 4.

7.2 Model output

The model outputs a vector of N path delays i and N complex values Ai(t) for every time instant. The

equivalent baseband channel impulse response is given by:

N

i ii ttAth1

)()(),( (31)

where t and indicate time and delay axes respectively. Note that the path delays i(t) are time-variant

and they can reach arbitrary values.

7.3 Model output usage

Let s(t) be the transmitted equivalent baseband signal, then the received signal r(t) can be calculated

in the usual way, by the convolution of the transmitted signal with the channel impulse response as:

r(t) = s(t) * h(t, ) (32)

The channel impulse responses as model output are updated at a rate given by sampf .

8 Wideband satellite-to-indoor channel propagation model

In § 7, a physical-statistical model for wideband simulations has been described that can be applied

to land-mobile situations. Within this section, we describe a simulation model that is able to simulate

the wideband satellite-to-indoor propagation scenario for receiver algorithm evaluations. In

particular, the model supports simulations for communications and for time-of-arrival estimation that

is needed in the field of positioning. Similar to § 7, the model provides the parameters of a linear

transversal filter that can be used to simulate the frequency-selective fading channel. Definitions on

terms related to multipath propagation are found in Recommendation ITU-R P.1407.

Rec. ITU-R P.681-11 31

The channel model provides simulations for the electromagnetic wave propagation from a satellite

based transmitter to a receiver that is located inside a building. A physical-statistical simulation

approach has been chosen, i.e. parts of the wave propagation channel are simulated using site specific

deterministic methods while other contributions are calculated based on modelled statistics that are

obtained from measurements. Measurements in that scope were performed at a carrier frequency of

1.51 GHz with a signal bandwidth of 100 MHz. The transmitter and the environment are assumed to

be static or quasi-static while the receiver position may vary with an arbitrary trajectory within a

scenery representing a room inside the building. The output will be a set of delays and complex

amplitudes for the different multipath components that can be used in a linear transversal filter

structure. The obtained parameters of the multipath components change coherently with the receiver

positions such that a spatially coherent simulation is supported.

The channel model consists of the following individual components to simulate the propagation

channel as illustrated in Fig. 22:

– Direct components: Representing multipath components that are passing through the outer

walls before they are directly received by the receive antenna. These components are based

on deterministic calculations using the structure of the scenery.

– Reflected components: Representing multipath components that are reflected by the interior

walls in the scenery. The delay and the angle-of-arrival of these components are simulated

using deterministic calculations while the complex amplitude is a stochastic variable.

– Scattered components: Representing multipath components in a completely stochastic

manner. All parameters of these components are simulated as random variables representing

interactions of the electromagnetic wave with internal objects like furniture for example.

FIGURE 22

Overview of individual components simulated within the satellite-to-indoor channel model

P.0681 22-

Window

Receiver

Direct components

Scatteredcomponents

Impinging planar wavefront

Reflectedcomponents

Multiple sIPscatteredcomponent

n1

n4

n3

n2

Transmitter

The model is split into an initialization and runtime phase as displayed in Fig. 23. During the

initialization phase the stochastics inside the channel model are initialized such that the runtime phase

is completely deterministic based on the drawn random variables. Therefore, the channel impulse

response depends only on the receiver position. In order to simulate a certain trajectory of the receiver,

the user should call the channel model in the runtime phase repeatedly with new receiver positions in

32 Rec. ITU-R P.681-11

a loop structure. As input of the channel model for the initialization phase, a description of the

scenery, the carrier frequency, the simulation bandwidth, the transmitter position and the root-mean-

square (rms) delay spread is expected. Optionally, the number of scattered components may be

provided. In terms of propagation parameters, the scenery description includes the perpendicular

transmission factors of materials which are the wall material and window glass. Values for the

perpendicular transmission coefficient and rms delay spread can be calculated from or found directly

in Recommendations ITU-R P.1238 and ITU-R P.2040.

The recommended method is incorporated in a computer program available as Supplement file

R-REC-P.681-11-201908-I!!!ZIP.

A complete description of the channel model including its implementation can be found in Report

ITU-R P.2145. During the runtime phase, receiver positions need to be supplied by the user within a

loop structure.

FIGURE 23

Overview of individual components simulated within the satellite-to-indoor channel model

P.0681 23-

Initialisation phaseParameters

Mu

ltip

ath

com

pone

nts

Receiver position

Transmitter position

Scenery definitionArtificial scenery

Power delay profile

Measurementsstatistics

Wall refl.model

Wall refl.model

Wall refl.model

Scatterermodel

Scatterermodel

Scatterermodel

Diffraction/transmission

Reflections Scatterers

Runtime phase

Direct components

8.1 Scope of the simulation model

The wideband satellite-to-indoor model is able to simulate a wideband satellite-to-indoor propagation

scenario for receiver algorithm evaluations. In particular, the model supports simulations for

communications and for time-of-arrival estimation is needed in the field of positioning.

8.2 Applicability of the model

The applicability of the model is limited in the following due to the stochastic parts obtained from

measurement data. In its current form, this limits the channel model to the following:

– Frequency range: 1 GHz to 2 GHz and for signal bandwidth of up to 100 MHz.

– Polarization: circular polarization.

– Environment: external facing rooms in typical office environments.

Due to the modelling approach, the wideband satellite-to-indoor model is restricted to:

– Static transmitter: the transmitter should be static or quasi static during the simulated time

period.

Rec. ITU-R P.681-11 33

– Room geometry: a single room with at least one wall facing the transmitter.

– Static environments: the environment is static and the receiver is the only moving object.

– Negligible outdoor reflections: Outdoor reflections that might occur due to other buildings

with similar heights in the vicinity are neglected.

8.3 Input Parameters

During the initialization phase, the wideband satellite-to-indoor channel model requires the following

input parameters:

Bandwidth Signal bandwidth in Hz.

Carrier frequency Carrier frequency in Hz.

Spatially averaged delay

spread

Delay spread in seconds. Delay spread is obtained averaging the power delay

profile over simulated space. The parameter defines the slope of the

exponential decreasing spatially averaged power delay profile. For delay

spread value, a formula and values can be found in Recommendation ITU-R

P.1238.

Transmitter position Three dimensional transmitter position in meters in the simulated reference

coordinate system provided by the scenery.

Scenery Defines the room layout that is needed for the physical deterministic part of

the channel model. Additionally, it also incorporates the perpendicular

transmission coefficients representing the materials for walls and windows.

Appropriate values can be calculated using the single-layer slab method in

Recommendation ITU-R P.2040.

Number of scattered

components

Optional parameter to change the simulated number of scattered components.

The default value is 10 000. Values should be larger than 1 000.

During the runtime phase the wideband satellite-to-indoor channel model, the following inputs are

required:

Receiver position Three dimensional receiver position in meters in the same coordinate system

as the transmitter position and the scenery. In order to simulate a certain

trajectory of the receiver, the user should call the routine of the channel

simulator repeatedly with new receiver positions in a loop structure.

8.4 Output Parameters

The model provides the channel impulse response (CIR) rx,h calculated based on the receiver

position rx provided to the user as:

,

1

0

rrr

r

xL

l

ll x~x~x,h (33)

where:

rxL number of visible paths at receiver position rx

rx~l complex amplitude of the path; it includes already the delay inside the phase

rx~l delay in seconds of the path normalized to the line-of-sight propagation time.

34 Rec. ITU-R P.681-11

9 Satellite diversity

In previous sections single satellite links have been considered. To improve availability, multiple

satellite systems may use link diversity. The combination/switching of signals from various satellites

is dealt with here. Two cases are considered, namely, the uncorrelated case where it is assumed that

shadowing effects affecting received signals from visible satellites are uncorrelated, and the

correlated case in which a given degree of correlation is present. In both situations multipath

originated signal variations are assumed to be uncorrelated.

9.1 Uncorrelated case

The model in § 6 has a capability for assessing satellite diversity effects in the case of multivisibility

satellite constellations (i.e. switching to the least impaired path). For GSO systems, the occurrence

probabilities of each state for each satellite link, i.e. PGOODn and PBADn (n 1, 2,..., N; N is number of

visible satellites) depend on each satellite elevation n State occurrence probabilities after the state-

selection diversity, PGOOD:div and PBAD:div are given by:

N

n

nGOODndivGOOD PP1

: )θ(–1–1 (34a)

PBAD:div =1– PGOOD:div (34b)

In the case of non-GSOs such as LEO and medium Earth orbit (MEO), the occurrence probabilities of the

various states for each satellite link vary with time depending on the time-varying satellite elevation. The

mean state occurrence probabilities, i.e. PGOOD:div and PBAD:div, after operating satellite diversity

from time t1 to t2 are as follows:

Pi:div =1

t2 – t1Pi:div (t) dt (i =GOOD,BAD)

t1

t2

ò (35)

9.2 Correlated case

In many instances, shadowing events affecting two links with a given angle spacing present some

degree of correlation that needs to be quantified in order to produce more accurate estimations of the

overall availability to be expected in a multiple satellite system. The shadowing cross-correlation

coefficient is used for this purpose. This parameter may take up values in the range of 1 going from

positive, close to 1, for small angle spacing to even negative for larger spacing.

9.2.1 Quantification of the shadowing cross-correlation coefficient in urban areas

Here, a simple three-segment model to quantify the cross-correlation coefficient between shadowing

events in urban areas is described. A canonical urban area geometry, the “street canyon” is used. The

objective is the quantification of the cross-correlation coefficient (), with being the angle spacing

between two separate satellite-to-mobile links in street canyons, which are described in terms of their

MKA.

Rec. ITU-R P.681-11 35

The geometry is indicated in Fig. 24 where:

1, 2 : satellite elevation angle

w : average street width

h : average building height

l : length of street under consideration.

FIGURE 24

Geometry of a street canyon

P.0681 24-

h

x1

2

2

l

w

Terminal

MKA

1

x2

1

The angle spacing between two links, , can be put in terms of more convenient angles: the elevations

of the two satellites, i and j, and their azimuth spacing, , i.e. the shadowing cross-correlation

coefficient can be expressed as (i, j, ).

Typical results obtained with this model are represented schematically in Fig. 25 which shows a

general behaviour with a three-segment pattern defined by points A, B, C and D. In addition to this

general pattern, there exist several special cases in which two or more of the four points merge.

Figure 24 shows that, in general, there usually exists a main lobe of positive, decreasing

cross-correlation values for small azimuth spacing (typically 30º) while, for larger values of ,

the coefficient tends to settle at a constant negative value. The lobe will present higher maxima when

the two satellites are at similar elevations. As the difference in elevations increases (i j), the lobe

will show much lower maxima.

36 Rec. ITU-R P.681-11

FIGURE 25

Three segment cross correlation coefficient model

P.0681 25-

1

0

–1

BA

Azimuth spacing (degrees)

Special case 1

Special case 2

Special case 3

General model

Special case 4

Co

rrel

atio

n c

oef

fici

ent,

0 10 20 30 40 50 60 70 80 90

C D

Special cases of this three-segment model have also been identified: special case 1 occurs when both

satellites are above the MKA for any azimuth spacing. In this case, the correlation coefficient takes

on a constant positive value of 1 for any . This is not a relevant case since, in this situation,

satellite diversity is not required. Special case 2 occurs when one satellite is always above MKA and

the other is always below (except at both ends of the canyon). In this case, the correlation coefficient

takes on a constant negative value. Special case 3 occurs when the two satellites are at the same

elevation. In this situation, the correlation lobe starts its decay from a maximum value of 1

(i.e. co-located satellites). This special case is applicable to those systems based on GSO satellites,

widely spaced in azimuth, but with very similar elevations. Finally, special case 4 occurs for satellites

with very different elevations (i j). Here, the correlation lobe extends across a much wider range

of azimuth spacings but showing small positive correlation values.

It must be pointed out that, given the geometry of the scenario (street canyon) and that it is assumed

that the user is in the middle of the street, correlation values are symmetric for all four quadrants;

this is the reason why only one quadrant is shown in Fig. 25.

With reference to Fig. 24, the following input data are used in the model: satellite elevations, 1 and

2 (degrees), average building height, h (m), average street width, w (m), and length of street under

consideration, l (m). A large value is advised for this last parameter, i.e. l 200 m. Further, it is

assumed that 2 1. The model azimuth spacing, , resolution is 1 and is valid for all frequency

bands although it becomes more accurate for bands above about 10 GHz.

The following steps shall be followed to calculate the cross-correlation coefficient values and azimuth

spacings corresponding to model points A, B, C and D:

Rec. ITU-R P.681-11 37

Step 1: Calculate auxiliary values x1, x2, M1 and M2 and angles 1 and 2 (see Fig. 24):

22

12

22

11

2tanand

2tan

whx

whx (36)

– If (x1,2)2 0 go to Step 6. This situation occurs when satellite 1 and/or 2 are always in line-of-

sight conditions for any azimuth spacing.

– If x1,2 l/2, make x1,2 l/2. This situation occurs when there is visibility for satellite 1 and/or

2 only at both ends of the street.

22

11

2/arctanroundand

2/arctanround

x

w

x

w (37)

90

5.0and

90

5.0 22

11

MM (38)

where “round” means rounded to the nearest integer value (degrees).

Step 2: Calculation of auxiliary information related to model points A and D.

For point A:

0)(42436024 101201200111 NNNN (39)

For point D:

– If 1 2 90,

24244443600 110201210011 NNNN (40a)

– If 1 2 > 90,

24360243600360444 210101002111 NNNN (40b)

Step 3: Calculation of the cross-correlation coefficient at points A and D:

)()(

)1()0()0()1()0()0()1()1(

359

1

21

2101211021002111

,

MMNMMNMMNMMN

DA (41)

359

)0()24360()1()24()(

211

211

12 MM

(42a)

359

)0()24360()1()24()(

222

222

22 MM

(42b)

Step 4: At point B, the correlation coefficient is the same as at point A and its azimuth spacing, ,

is given by:

Azimuth 12BPoint degrees (43)

38 Rec. ITU-R P.681-11

Step 5: At point C, the correlation coefficient is the same as at point D and its azimuth spacing, ,

is given by:

– If 1 2 90, Azimuth 21CPoint degrees (44a)

– If 1 2 90, 21CPoint 180 Azimuth degrees (44b)

Step 6: This is the case in which, for one or both elevations, there are always line-of-sight conditions.

Here, the correlation coefficient is calculated in a slightly different manner to that in Step 3:

– If both satellites are always visible, the cross-correlation coefficient is constant and equal

to 1 for any .

– If one of the satellites is always visible, the cross-correlation coefficient is also constant and

is given by:

1

180

11N (45)

where N11 41 2, and 1 is calculated as in Step 1.

9.2.2 Availability calculations

Once the cross-correlation coefficient is available, it is possible to compute the availability

improvement introduced by the use of satellite diversity. Here, expressions to calculate the system

availability for the two-satellite diversity case are provided. Given the usually small margins (or

power control ranges) used in land mobile satellite systems, only shadowing effects need to be

considered. This is a reasonable working hypothesis since availability events will correspond to links

in line-of-sight conditions in which case multipath-originated variations are Ricean and thus, fairly

small. In the case of shadowed conditions (heavy or light), the links will be in an outage state even if

multipath gives rise to significant signal enhancements.

Given two angle spaced links with unavailability probabilities, p1 and p2, and a shadowing cross-

correlation coefficient , the overall availability improbability after satellite diversity is given by:

2121110 )1()1( ppppppp (46)

and the probability of availability will be 1 – p0. Valid values of in equation (46) are limited to those

rendering non-negative values for p0. Probabilities p1 and p2, for urban areas can be computed by

using the model given in § 4.2.

Overall calculations for a given time interval or for a complete constellation period require the

computation of weighted averages over all positions (azimuths and elevations) of the two satellites

with respect to the user terminal.

9.3 Modelling satellite diversity effects using MKFs

MKFs as defined in § 4.4 can be used in the calculation of multi-satellite availabilities. Possible

partial correlation of blockage effects between the various links is already contained in the geometry

of the masks themselves. In Fig. 26 the calculation of the availability of a system comprising two

GSO satellites is illustrated. Lines A-B and C-D indicate the sweep paths to be followed for the

calculation of the combined availability. Line A-B indicates the 360º azimuth sweep at elevation 1

corresponding to satellite-1 and line C-D indicates the 360º azimuth sweep at elevation 2 for

Rec. ITU-R P.681-11 39

satellite-2. To account for the possible blockage cross-correlation the 360º sweep must be carried out

preserving the azimuth spacing, , between the two satellites.

The use of the street MKFs can also be extended to multiple GSO satellites and to the case of

non-GSO constellations. In the last case, the study would consist in the repeated computation of 360º

street orientation sweeps for a sufficiently large number of satellite constellation snapshots.

A snapshot in this context indicates the instantaneous positions (azimuths and elevations) of the

various satellites above a minimum operational elevation, min. By defining an appropriate stepping

interval, T, and observation period, Tobs, the availability can be can be calculated as the time-, street

orientation-weighed average of the obtained results in each snapshot. Values of T 1 min and Tobs

equal to the constellation period provide adequate results.

FIGURE 26

Calculation of total system availability for a constellation

of two GSO satellites with respect to a T-junction

P.0681 26-

80

60

40

20

0

20

40

60

80

160

–160

180

–180

140

–140

120

–120

100

–100

60

–60

40

–40

20

–20

0

0

80

–80

D

B

C

D

BA

Azimuth (degrees)

MKF, T-junction

Azimuth sweep,

Ele

vat

ion

(de

gre

es)

C

AFrom satellite-2

From satellite-1

Annex 2

1 Introduction

Input parameters for the statistical and generative narrowband models described in § 6 of Annex 1

are provided hereafter for various ranges of frequencies and environments. Available parameters sets

are summarized in Tables 7 to 10.

The parameters are presented following the format of Table 7:

40 Rec. ITU-R P.681-11

TABLE 7

Input parameters data format

Frequency/ environment / elevation angle (degrees)

Information Useful details about the area or the device

used for the channel characterization

Parameter Good Bad

(µ,)G,B µ G, G µB,B

durminG,B durminG durminB

( μ𝑀𝐴 GB, σ𝑀𝐴 GB) μ𝑀𝐴 G, σ𝑀𝐴 G μ𝑀𝐴 B, σ𝑀𝐴 B

MPG,B h1G, h2G h1B, h2B

∑AG,B g1G , g2G g1B, g2,B

LcorrG,B* LcorrG Lcorr,B

f1ΔMA + f2 f1, f2

[pB,min , pB,max] Probability range to consider for the MA B

distribution

Remark: G stands for the GOOD state and B stands for the BAD state.

* Only for generative modeling.

TABLE 8

Model parameters for frequencies between 1.5 and 3 GHz

Environment Elevation angle (degrees)

Urban 20 30 45 60 70

Suburban 20 30 45 60 70

Village 20 30 45 60 70

Rural wooded 20 30 45 60 70

Residential 20 30 – 60 70

Rec. ITU-R P.681-11 41

TABLE 9

Model parameters for frequencies between 3 and 5 GHz

Environment Elevation angle (degrees)

Urban 20 30 45 60 70

Suburban 20 30 45 60 70

Village 20 30 45 60 70

Rural wooded 20 30 45 60 70

Residential 20 30 – 60 70

TABLE 10

Model parameters for frequencies between 10 and 20 GHz

Environment Elevation angle (degrees)

Suburban 30, 34

Rural 34

Highway 30

Railway 30

Urban 30

2 Frequencies between 1.5 and 3 GHz

2.1 Urban environment

2.2 GHz/ Urban / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.0042 1.2049 3.689 0.9796

durminG,B 3.9889 10.3114

μ𝑀𝐴 GB, σ𝑀𝐴 GB –3.3681 3.3226 –18.1771 3.2672

h1G,B, h2G,B 0.1739 –11.5966 1.1411 4.0581

g1G,B, g2G,B 0.0036 1.3230 –0.2502 –1.2528

LcorrG,B 0.9680 0.9680

f1ΔMA+f2 0.0870 2.8469

[pB,min , pB,max] [0.1 ; 0.9]

42 Rec. ITU-R P.681-11

2.2 GHz/ Urban / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in and around a typical medium-sized city in France

Parameter GOOD BAD

µ G,B,G,B 2.7332 1.1030 2.7582 1.2210

durminG,B 7.3174 5.7276

μ𝑀𝐴 GB, σ𝑀𝐴 GB –2.3773 2.1222 –17.4276 3.9532

h1G,B, h2G,B 0.0941 –13.1679 0.9175 –0.8009

g1G,B, g2G,B –0.2811 0.9323 –0.1484 0.5910

LcorrG,B 1.4731 1.4731

f1ΔMA+f2 0.1378 3.3733

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Urban / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.0639 1.6980 2.9108 1.2602

durminG,B 10.0 6.0

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.8225 1.1317 –15.4844 3.3245

h1G,B, h2G,B –0.0481 –14.7450 0.9434 –1.7555

g1G,B, g2G,B –0.4643 0.3334 –0.0798 2.8101

LcorrG,B 1.7910 1.7910

f1ΔMA+f2 0.0744 2.1423

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Urban / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.8135 1.5962 2.0211 0.6568

durminG,B 10.0 1.9126

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.5872 1.2446 –14.1435 3.2706

h1G,B, h2G,B –0.5168 –17.4060 0.6975 –7.5383

g1G,B, g2G,B –0.1953 0.5353 0.0422 3.2030

LcorrG,B 1.7977 1.7977

f1ΔMA+f2 –0.1285 5.4991

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 43

2.2 GHz/ Urban / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.2919 2.4703 2.1012 1.0341

durminG,B 118.3312 4.8569

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.8434 0.5370 –12.9383 1.7588

h1G,B, h2G,B –4.7301 –26.5687 2.5318 16.8468

g1G,B, g2G,B 0.5192 1.9583 0.3768 8.4377

LcorrG,B 2.0963 2.0963

f1ΔMA+f2 –0.0826 2.8824

[pB,min , pB,max] [0.1 ; 0.9]

2.2 Suburban environment

2.2 GHz/ Suburban / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.2201 1.2767 2.2657 1.3812

durminG,B 2.2914 2.5585

μ𝑀𝐴 GB, σ𝑀𝐴 GB –2.7191 1.3840 –13.8808 2.5830

h1G,B, h2G,B –0.3037 –13.0719 1.0136 0.5158

g1G,B, g2G,B –0.1254 0.7894 –0.1441 0.7757

LcorrG,B 0.9290 0.9290

f1ΔMA+f2 0.2904 1.0324

[pB,min , pB,max] [0.1 ; 0.9]

44 Rec. ITU-R P.681-11

2.2 GHz/ Suburban / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.0138 1.4161 2.4521 0.7637

durminG,B 8.3214 5.9087

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.7018 1.2107 –11.9823 3.4728

h1G,B, h2G,B –0.6543 –14.6457 0.6200 –7.5485

g1G,B, g2G,B –0.1333 0.8992 –0.1644 0.2762

LcorrG,B 1.7135 1.7135

f1ΔMA+f2 0.1091 3.3000

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Suburban / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.5857 1.3918 2.2414 0.7884

durminG,B 126.8375 4.3132

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.1496 1.0369 –10.3806 2.3543

h1G,B, h2G,B 0.2148 –17.8462 0.0344 –14.2087

g1G,B, g2G,B 0.0729 1.0303 0.0662 3.5043

LcorrG,B 3.2293 3.2293

f1ΔMA+f2 0.5766 0.7163

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Suburban / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.4124 1.4331 1.9922 0.7132

durminG,B 19.5431 3.1213

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.7811 0.7979 –12.1436 3.1798

h1G,B, h2G,B –2.1102 –19.7954 0.4372 –8.3651

g1G,B, g2G,B –0.2284 0.2796 –0.2903 –0.6001

LcorrG,B 2.0215 2.0215

f1ΔMA+f2 –0.4097 8.7440

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 45

2.2 GHz/ Suburban / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.2919 2.4703 2.1012 1.0341

durminG,B 118.3312 4.8569

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.8434 0.5370 –12.9383 1.7588

h1G,B, h2G,B –4.7301 –26.5687 2.5318 16.8468

g1G,B, g2G,B 0.5192 1.9583 0.3768 8.4377

LcorrG,B 2.0963 2.0963

f1ΔMA+f2 –0.0826 2.8824

[pB,min , pB,max] [0.1 ; 0.9]

2.3 Village environment

2.2 GHz/ Village / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.7663 1.1211 2.2328 1.3788

durminG,B 6.5373 2.8174

μ𝑀𝐴 GB, σ𝑀𝐴 GB –2.5017 2.3059 –15.2300 5.0919

h1G,B, h2G,B 0.0238 –11.4824 0.9971 0.8970

g1G,B, g2G,B –0.2735 1.3898 –0.0568 1.9253

LcorrG,B 0.8574 0.8574

f1ΔMA+f2 0.0644 2.6740

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Village / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.4246 1.3025 1.8980 1.0505

durminG,B 5.4326 2.4696

h1G,B, h2G,B –2.2284 1.4984 –15.1583 4.0987

g1G,B, g2G,B –0.3431 –14.0798 0.9614 0.3719

h1G,B, h2G,B –0.2215 1.0077 –0.0961 1.3123

LcorrG,B 0.8264 0.8264

f1ΔMA+f2 –0.0576 3.3977

[pB,min , pB,max] [0.1 ; 0.9]

46 Rec. ITU-R P.681-11

2.2 GHz/ Village / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.8402 1.4563 1.8509 0.8736

durminG,B 10.4906 2.6515

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.2871 0.6346 –12.6718 3.1722

h1G,B, h2G,B –0.0222 –16.7316 0.8329 –3.9947

g1G,B, g2G,B –0.3905 0.4880 –0.0980 1.3381

LcorrG,B 1.4256 1.4256

f1ΔMA+f2 –0.0493 5.3952

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Village / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.7630 1.2854 1.7192 1.1420

durminG,B 17.6726 2.5981

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.5364 0.6115 –9.5399 2.0732

h1G,B, h2G,B –0.1418 –17.8032 –0.4454 –16.8201

g1G,B, g2G,B –0.2120 0.7819 0.0609 2.5925

LcorrG,B 0.8830 0.8830

f1ΔMA+f2 –0.8818 10.1610

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Village / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.0717 1.2475 1.5673 0.5948

durminG,B 30.8829 2.1609

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.3340 0.6279 –8.3686 2.5603

h1G,B, h2G,B –1.6253 –19.7558 0.1788 –9.5153

g1G,B, g2G,B –0.4438 0.6355 –0.0779 1.1209

LcorrG,B 1.5633 1.5633

f1ΔMA+f2 –0.3483 5.1244

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 47

2.4 Rural wooded environment

2.2 GHz/ Rural wooded / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.1597 1.3766 1.9587 1.5465

durminG,B 2.0744 1.3934

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.8065 1.5635 –10.6615 2.6170

h1G,B, h2G,B –0.9170 –12.1228 0.8440 –1.4804

g1G,B, g2G,B –0.0348 0.9571 –0.1069 1.6141

LcorrG,B 0.8845 0.8845

f1ΔMA+f2 0.0550 2.6383

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Rural wooded / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.5579 1.2444 2.3791 1.1778

durminG,B 3.5947 2.2800

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.3214 1.6645 –10.4240 2.4446

h1G,B, h2G,B –1.0445 –14.3176 0.6278 –4.8146

g1G,B, g2G,B –0.1656 0.7180 –0.0451 2.2327

LcorrG,B 1.0942 1.0942

f1ΔMA+f2 0.0256 3.8527

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Wooded / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.1803 1.3427 2.5382 1.1291

durminG,B 6.7673 3.3683

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.9902 1.0348 –10.2891 2.3090

h1G,B, h2G,B –0.4235 –16.8380 0.3386 –9.7118

g1G,B, g2G,B –0.1095 0.6893 –0.0460 2.1310

LcorrG,B 2.3956 2.3956

f1ΔMA+f2 0.2803 4.0004

[pB,min , pB,max] [0.1 ; 0.9]

48 Rec. ITU-R P.681-11

2.2 GHz/ Rural wooded / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.9322 1.3234 2.1955 1.1115

durminG,B 5.7209 1.6512

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.6153 1.1723 –9.9595 2.2188

h1G,B, h2G,B –1.4024 –16.9664 0.2666 –9.0046

g1G,B, g2G,B –0.2516 0.5353 –0.0907 1.4730

LcorrG,B 1.7586 1.7586

f1ΔMA+f2 0.1099 4.2183

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Rural wooded / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.8768 1.4738 1.8445 0.8874

durminG,B 16.0855 2.9629

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.7818 0.7044 –6.7769 2.1339

h1G,B, h2G,B –2.9566 –20.0326 –0.3723 –14.9638

g1G,B, g2G,B –0.2874 0.4050 –0.1822 0.1163

LcorrG,B 1.6546 1.6546

f1ΔMA+f2 –0.3914 6.6931

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 49

2.5 Residential environment

2.2 GHz/ Residential / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.5818 1.7310 1.7136 1.1421

durminG,B 9.2291 1.6385

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.8449 1.3050 –10.8315 2.2642

h1G,B, h2G,B –0.3977 –12.3714 0.8589 –2.4054

g1G,B, g2G,B 0.0984 1.3138 –0.1804 0.8553

LcorrG,B 1.1578 1.1578

f1ΔMA+f2 0.0994 2.4200

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Residential / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.2810 1.4200 1.8414 0.9697

durminG,B 14.4825 2.7681

μ𝑀𝐴 GB, σ𝑀𝐴 GB –1.3799 1.0010 –11.1669 2.4724

h1G,B, h2G,B –0.8893 –16.4615 –0.1030 –13.7102

g1G,B, g2G,B –0.2432 0.6519 –0.1025 1.7671

LcorrG,B 1.9053 1.9053

f1ΔMA+f2 0.0196 3.9374

[pB,min , pB,max] [0.1 ; 0.9]

2.2 GHz/ Residential / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.255 1.287 3.277 1.260

durminG,B 6.47 7.81

μ𝑀𝐴 GB, σ𝑀𝐴 GB 0 0.30 –2.32 2.06

h1G,B, h2G,B –2.024 –19.454 –1.496 –22.894

g1G,B, g2G,B 0.273 0.403 –0.361 –0.119

LcorrG,B 3.84 3.84

f1ΔMA+f2 –1.591 12.274

[pB,min , pB,max] [0.1 ; 0.9]

50 Rec. ITU-R P.681-11

2.2 GHz/ Residential / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.3291 0.7249 3.4534 0.9763

durminG,B 27.3637 8.9481

μ𝑀𝐴 GB, σ𝑀𝐴 GB –0.1625 0.3249 –1.6084 0.5817

h1G,B, h2G,B 0.6321 –21.5594 –0.3976 –22.7905

g1G,B, g2G,B 0.1764 0.4135 –0.0796 0.1939

LcorrG,B 1.6854 1.6854

f1ΔMA+f2 3.0127 6.2345

[pB,min , pB,max] [0.1 ; 0.9]

3 Frequencies between 3 and 5 GHz

3.1 Urban environment

3.8 GHz/ Urban / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µG,B,G,B 2.5467 1.0431 3.6890 0.9796

durminG,B 5.2610 10.3114

μ𝑀𝐴 GB, σ𝑀𝐴 GB −2.7844 2.6841 −19.4022 3.2428

h1G,B, h2G,B 0.1757 −12.9417 0.9638 −0.9382

g1G,B, g2G,B −0.2044 1.5866 0.0537 4.5670

LcorrG,B 1.4243 1.4243

f1ΔMA+f2 0.1073 1.9199

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 51

3.8 GHz/ Urban / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µG,B,G,B 2.0158 1.2348 2.2627 1.4901

durminG,B 4.5491 2.0749

μ𝑀𝐴 GB, σ𝑀𝐴 GB −3.7749 2.2381 −17.9098 2.9828

h1G,B, h2G,B −0.1564 −15.1531 0.8250 −2.5833

g1G,B, g2G,B −0.0343 1.0602 −0.0741 2.1406

LcorrG,B 0.8999 0.8999

f1ΔMA+f2 0.2707 -0.0287

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Urban / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µG,B,G,B 2.3005 1.6960 2.6314 1.1210

durminG,B 10.0 6.0

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.4466 1.1472 −15.3926 3.2527

h1G,B, h2G,B 0.1550 −13.6861 0.9509 −1.2462

g1G,B, g2G,B 0.1666 1.2558 0.0363 4.4356

LcorrG,B 1.6424 1.6424

f1ΔMA+f2 0.2517 −0.3512

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Urban / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µG,B,G,B 2.4546 1.9595 1.8892 0.8982

durminG,B 10.0 1.9126

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.6655 0.8244 −14.4922 3.4941

h1G,B, h2G,B −0.4887 −17.2505 0.4501 −9.6935

g1G,B, g2G,B −0.3373 0.3285 0.1202 4.8329

LcorrG,B 2.3036 2.3036

f1ΔMA+f2 0.0025 1.4949

[pB,min , pB,max] [0.1 ; 0.9]

52 Rec. ITU-R P.681-11

3.8 GHz/ Urban / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µG,B,G,B 2.8354 2.4631 1.5170 1.1057

durminG,B 67.5721 3.6673

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.0455 0.2934 −14.2294 5.4444

h1G,B, h2G,B −3.0973 −20.7862 0.0908 −15.8022

g1G,B, g2G,B 0.0808 0.8952 0.0065 3.1520

LcorrG,B 2.2062 2.2062

f1ΔMA+f2 0.0755 2.1426

[pB,min , pB,max] [0.1 ; 0.9]

3.2 Suburban environment

3.8 GHz/ Suburban / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.8194 1.6507 2.5873 1.3919

durminG,B 11.1083 4.4393

μ𝑀𝐴 GB, σ𝑀𝐴 GB −4.8136 1.9133 −17.0970 2.9350

h1G,B, h2G,B −0.4500 -17.9227 0.8991 −2.4082

g1G,B, g2G,B −0.1763 0.8244 0.0582 4.0347

LcorrG,B 1.2571 1.2571

f1ΔMA+f2 0.0727 2.8177

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Suburban / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.9226 1.3840 2.7375 0.6890

durminG,B 6.7899 7.7356

h1G,B, h2G,B −1.9611 1.8460 −15.3022 2.9379

g1G,B, g2G,B 0.2329 −15.0063 0.5146 −8.9987

h1G,B, h2G,B 0.0334 1.3323 0.0880 4.4692

LcorrG,B 1.6156 1.6156

f1ΔMA+f2 0.1281 2.3949

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 53

3.8 GHz/ Suburban / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.3019 0.8530 2.3715 1.3435

durminG,B 36.1277 9.5511

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.2730 0.9286 −5.6373 2.9302

h1G,B, h2G,B 0.2050 −17.5670 −0.7188 −21.0513

g1G,B, g2G,B 0.0074 0.7490 −0.2896 −0.3951

LcorrG,B 1.1191 1.1191

f1ΔMA+f2 −0.9586 10.8084

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Suburban / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.8958 1.7061 1.9128 0.6869

durminG,B 13.9133 2.9398

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.1987 1.0492 −13.1811 2.6228

h1G,B, h2G,B −1.6501 −18.9375 0.6911 −6.0721

g1G,B, g2G,B −0.1369 0.4477 0.0598 3.7220

LcorrG,B 3.0619 3.0619

f1ΔMA+f2 −0.0419 5.8920

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Suburban / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 4.1684 1.0766 1.4778 0.7033

durminG,B 42.0185 1.8473

μ𝑀𝐴 GB, σ𝑀𝐴 GB 0.1600 0.5082 −10.2225 1.8417

h1G,B, h2G,B −3.4369 −18.1632 0.3934 −9.6284

g1G,B, g2G,B −1.1144 0.9703 −0.1331 0.7223

LcorrG,B 2.5817 2.5817

f1ΔMA+f2 −0.1129 4.0555

[pB,min , pB,max] [0.1 ; 0.9]

54 Rec. ITU-R P.681-11

3.3 Village environment

3.8 GHz/ Village / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.0262 1.2355 1.9451 1.4293

durminG,B 2.2401 1.9624

𝜇𝑀𝐴 GB, σ𝑀𝐴 GB −3.1324 1.8929 −16.5697 4.0368

h1G,B, h2G,B −0.4368 −15.1009 1.0921 1.6440

g1G,B, g2G,B −0.0423 1.2532 −0.0325 2.4452

LcorrG,B 0.8380 0.8380

f1ΔMA+f2 0.0590 1.5623

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Village / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.4504 1.1061 1.7813 1.2802

durminG,B 2.3941 2.1484

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.8384 1.7960 −15.4143 4.5579

h1G,B, h2G,B −0.5582 −14.4416 0.8549 −2.2415

g1G,B, g2G,B −0.4545 0.8188 −0.0761 1.6768

LcorrG,B 0.9268 0.9268

f1ΔMA+f2 −0.0330 2.7056

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Village / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.2910 1.4229 1.2738 1.1539

durminG,B 2.8605 0.7797

μ𝑀𝐴 GB, σ𝑀𝐴 GB −0.0018 1.1193 −12.1063 2.9814

h1G,B, h2G,B −1.2023 −14.0732 0.6537 −4.5948

g1G,B, g2G,B −0.1033 0.9299 −0.0815 1.6693

LcorrG,B 0.9288 0.9288

f1ΔMA+f2 0.0002 1.9694

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 55

3.8 GHz/ Village / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.0956 1.3725 1.0920 1.2080

durminG,B 8.1516 0.7934

μ𝑀𝐴 GB, σ𝑀𝐴 GB −0.5220 1.0950 −12.1817 3.3604

h1G,B, h2G,B 0.0831 −16.8546 1.1006 0.5381

g1G,B, g2G,B 0.0411 1.1482 −0.0098 2.4287

LcorrG,B 1.2251 1.2251

f1ΔMA+f2 −0.0530 2.7165

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Village / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.9982 1.3320 1.4165 0.4685

durminG,B 28.3220 2.5168

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.3403 0.7793 −11.9560 1.5654

h1G,B, h2G,B −0.4861 −19.5316 0.5663 −6.8615

g1G,B, g2G,B −0.2356 0.7178 −0.2903 −1.2715

LcorrG,B 1.4378 1.4378

f1ΔMA+f2 −0.0983 3.9005

[pB,min , pB,max] [0.1 ; 0.9]

56 Rec. ITU-R P.681-11

3.4 Rural wooded environment

3.8 GHz/ Rural wooded / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.0294 1.4280 2.0290 1.5493

durminG,B 1.7836 1.5269

μ𝑀𝐴 GB, σ𝑀𝐴 GB −3.2536 1.6159 −14.3363 2.7753

h1G,B, h2G,B −0.5718 −16.1382 0.8186 −2.9963

g1G,B, g2G,B −0.0805 0.9430 −0.0822 1.7660

LcorrG,B 1.0863 1.0863

f1ΔMA+f2 0.1263 1.4478

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Rural wooded / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.1218 1.4895 2.2051 1.5741

durminG,B 2.4539 2.1289

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.5431 1.8811 −12.8884 3.0097

h1G,B, h2G,B −0.7288 −14.1626 0.6635 −4.6034

g1G,B, g2G,B −0.1241 0.9482 −0.0634 2.3898

LcorrG,B 1.3253 1.3253

f1ΔMA+f2 0.0849 1.6324

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Rural wooded / 45 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.1803 1.3427 2.4017 1.1315

durminG,B 6.7673 3.5668

μ𝑀𝐴 GB, σ𝑀𝐴 GB 0.0428 1.6768 −11.3173 2.7467

h1G,B, h2G,B −0.9948 −14.4265 0.2929 −9.7910

g1G,B, g2G,B −0.1377 1.0077 −0.0387 2.6194

LcorrG,B 2.0419 2.0419

f1ΔMA+f2 0.1894 2.1378

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 57

3.8 GHz/ Rural wooded / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.4961 1.4379 2.2113 1.1254

durminG,B 3.7229 1.9001

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.0828 1.0022 −12.3044 2.3641

h1G,B, h2G,B −1.2973 −16.6791 0.5456 −6.4660

g1G,B, g2G,B −0.1187 0.6254 −0.0443 2.3029

LcorrG,B 1.9038 1.9038

f1ΔMA+f2 0.1624 1.8417

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Rural wooded / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.8382 1.3804 2.1470 1.0038

durminG,B 6.8051 1.9195

μ𝑀𝐴 GB, σ𝑀𝐴 GB −0.8923 0.9455 −11.5722 2.3437

h1G,B, h2G,B −1.3425 −17.5636 0.3459 −9.5399

g1G,B, g2G,B −0.1210 0.6444 −0.0275 2.6238

LcorrG,B 2.1466 2.1466

f1ΔMA+f2 0.0593 2.8854

[pB,min , pB,max] [0.1 ; 0.9]

3.5 Residential environment

3.8 GHz/ Residential / 20 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.9050 1.7236 2.1969 0.9865

durminG,B 10.7373 2.2901

μ𝑀𝐴 GB, σ𝑀𝐴 GB −1.4426 1.2989 −14.4036 3.0396

h1G,B, h2G,B 0.4875 −13.5981 0.5813 −6.9790

g1G,B, g2G,B 0.1343 1.8247 −0.0911 2.1475

LcorrG,B 1.2788 1.2788

f1ΔMA+f2 0.2334 0.7612

[pB,min , pB,max] [0.1 ; 0.9]

58 Rec. ITU-R P.681-11

3.8 GHz/ Residential / 30 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.7334 1.6971 1.8403 0.9268

durminG,B 10.2996 1.8073

μ𝑀𝐴 GB, σ𝑀𝐴 GB −0.9996 1.0752 −12.9855 2.8149

h1G,B, h2G,B 0.3407 −14.8465 0.3553 −9.9284

g1G,B, g2G,B −0.0413 1.2006 0.0501 3.8667

LcorrG,B 1.7072 1.7072

f1ΔMA+f2 0.0443 2.2591

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Residential / 60 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 3.4044 1.3980 2.5534 1.7143

durminG,B 10.4862 4.7289

μ𝑀𝐴 GB, σ𝑀𝐴 GB 0.4640 0.7060 −2.3787 0.8123

h1G,B, h2G,B 0.3710 −19.6032 −2.3834 −24.6987

g1G,B, g2G,B 0.0332 0.5053 0.0172 0.7237

LcorrG,B 1.8017 1.8017

f1ΔMA+f2 3.1149 3.5721

[pB,min , pB,max] [0.1 ; 0.9]

3.8 GHz/ Residential / 70 degrees

Information

Antenna gain < 5 dBi / Measurements performed with

an helicopter in and around a typical medium-sized city

in France

Parameter GOOD BAD

µ G,B,G,B 2.9223 1.0267 2.5188 1.3166

durminG,B 7.3764 7.2801

μ𝑀𝐴 GB, σ𝑀𝐴 GB −0.1628 0.5104 −2.3703 1.5998

h1G,B, h2G,B 0.1590 −20.4767 −1.0228 −22.4769

g1G,B, g2G,B 0.1137 0.4579 −0.0986 0.2879

LcorrG,B 1.3531 1.3531

f1ΔMA+f2 −0.0538 5.1204

[pB,min , pB,max] [0.1 ; 0.9]

Rec. ITU-R P.681-11 59

4 Frequencies between 10 and 20 GHz

4.1 Rural environment

11.7 GHz/ Rural / 34 degrees

Information Antenna gain = 19 dBi / Measurements performed with a

satellite around a typical large-sized city in Germany

Parameter GOOD BAD

µ G,B,G,B 1.7663 1.9350 −0.4722 1.7232

durminG,B 0.9 0.8

μ𝑀𝐴 GB, σ𝑀𝐴 GB 0.05 0 −16 10.4

h1G,B, h2G,B 0 −40.25 0.87 −14.26

g1G,B, g2G,B 0 0.39 −0.21 0

LcorrG,B 0.5 0.5

f1ΔMA+f2 0.088 1.21

[pB,min , pB,max] [0.1 ; 0.9]

4.2 Suburban environment

For the suburban environment, as two tables are available, the table with the closest frequency from

the frequency of interest should be used.

11.7 GHz/ Suburban / 34 degrees

Information Antenna gain = 19 dBi / Measurements performed with a

satellite around a typical large-sized city in Germany

Parameter GOOD BAD

µ G,B,G,B 1.0125 1.6944 −0.8026 1.288

durminG,B 1.5 1.1

μ𝑀𝐴 GB, σ𝑀𝐴 GB −0.02 0 −5.4 7.3

h1G,B, h2G,B 0 −38.17 0.69 −15.97

g1G,B, g2G,B 0 0.39 −0.21 0

LcorrG,B 0.5 0.5

f1ΔMA+f2 0.036 0.80

[pB,min , pB,max] [0.1 ; 0.6]

60 Rec. ITU-R P.681-11

20 GHz/ Suburban / 30 degrees

Information Antenna gain = 31 dBi / Measurements performed with a

satellite around a typical large-sized city in France

Parameter GOOD BAD

µ G,B,G,B 1.66 1.64 0.10 1.70

durminG,B 0.01 0.5

μ𝑀𝐴𝐺𝐵, σ𝑀𝐴𝐺𝐵 −0.23 0.49 −8.93 8.41

h1G,B, h2G,B 0 −30.99 0.48 −11.37

g1G,B, g2G,B 0 0.49 −0.45 0

LcorrG,B 7.9 7.9

f1ΔMA+f2 0.08 1.67

[pB,min , pB,max] [0.006 ; 0.921]

4.3 Highway environment

20 GHz/ Highway / 30 degrees

Information Antenna gain = 31 dBi / Measurements performed with a

satellite around a typical large-sized city in France

Parameter GOOD BAD

µ G,B,G,B 1.27 1.86 −0.31 1.35

durminG,B 0.01 0.5

μ𝑀𝐴𝐺𝐵, σ𝑀𝐴𝐺𝐵 −0.16 0.39 −5.92 8.20

h1G,B, h2G,B 0.00 −29.61 0.34 −14.39

g1G,B, g2G,B 0.00 0.39 −0.41 0.00

LcorrG,B 31.7 31.7

f1ΔMA+f2 0.15 1.28

[pB,min , pB,max] [0.001 ; 0.861]

Rec. ITU-R P.681-11 61

4.4 Urban environment

20 GHz/ Urban / 30 degrees

Information Antenna gain = 31 dBi / Measurements performed with a

satellite around a typical large-sized city in France

Parameter GOOD BAD

µ G,B,G,B 1.95 1.82 0.05 1.40

durminG,B 0.01 1

μ𝑀𝐴𝐺𝐵, σ𝑀𝐴𝐺𝐵 −0.21 0.44 −13.96 8.93

h1G,B, h2G,B 0 −32.62 0.68 −10.06

g1G,B, g2G,B 0 0.44 −0.37 0

LcorrG,B 5.67 5.67

f1ΔMA+f2 0.10 1.49

[pB,min , pB,max] [0.03 ; 0.97]

4.5 Train environment

20 GHz/ Train / 30 degrees

Information Antenna gain = 31 dBi / Measurements performed with a

satellite around a typical large-sized city in France

Parameter GOOD BAD

µ G,B,G,B 1.37 1.94 −0.02 1.92

durminG,B 0.01 0.5

μ𝑀𝐴𝐺𝐵, σ𝑀𝐴𝐺𝐵 −0.19 0.47 −5.84 7.47

h1G,B, h2G,B 0 −26.07 0.47 −12.78

g1G,B, g2G,B 0 0.47 −0.41 0

LcorrG,B 19.52 19.52

f1ΔMA+f2 0.12 1.78

[pB,min , pB,max] [0.0006 ; 0.88]